The movement of a low-viscosity crustal layer in response to topographic loading provides a potential mechanism for (1) eastward flow of the Asian lower crust causing the peripheral growth of the Tibetan Plateau and (2) southward flow of the Indian middle crust to be extruded along the Himalayan topographic front. Thermomechanical models for channel flow link such extrusion to focused orographic precipitation at the surface. Isotopic constraints on the timing of fault movement, anatexis and thermobarometric evolution of the exhumed garnet- to sillimanite-grade metasedimentary rocks support mid-crustal channel flow during the Early to Mid-Miocene. Exhumed metamorphic assemblages suggest that the dominant mechanism of the viscosity reduction that is a requirement for channel flow was melt weakening along the upper surface, defined by the South Tibetan Detachment System, and strain softening along the base, bounded by the Main Central Thrust. Neotectonic extrusion, bounded by brittle Quaternary faults south of the Main Central Thrust, is positively correlated with the spatial distribution of precipitation across a north–south transect, suggesting climate–tectonic linkage over a million-year time scale. A proposed orogen-wide eastward increase in extrusion rate over 20 Ma reflects current precipitation patterns but climate–tectonic linkage over this time scale remains equivocal.